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Information × Registration Number 0219U003520, 0116U000823 , R & D reports Title Studies in qualitative behavior of dynamical systems of various nature popup.stage_title Head Korobov Valerii, Registration Date 17-01-2019 Organization Kharkov National University named after V.N. Karazin popup.description2 Object of the research - dynamical systems arising in problems of mathematical physics, the control theory, the fluid mechanics, differential geometry. Aim of the research - creation of effective methods for the study of the qualitative behavior of solutions of dynamical systems arising in problems of mathematical physics, the fluid mechanics, the control theory etc. Methods of the research - methods of the general and qualitative theory of differential equations, the control theory, mathematical physics, continuum mechanics., differential geometry and topology. Within the research: nonlinear PDE with discrete state-dependent delay are studied; existence and uniqueness of solutions for initial functions from a Banach space are proved, global properties of classical solutions are studied; new methods of solving systems of almost polynomial equations and the corresponding time optimal control problems are proposed; the conditions for coincidence of equivalence in the sense of time optimality and algebraic equivalence are found for systems affine on control; wave flows of viscous liquid in systems of reservoirs with walls made of bioactive materials are studied; a model of passive and active regulation of reservoir geometry in dependence of values and time derivatives of pressure in it and a concentration of bioactive chemical agents is proposed; an affine classification of points of three-dimensional surfaces in a six-dimensional Euclidean space in terms of an indicatrix of normal curvature is given; criterions of conservation of horizontal mean curvature of a hypersurface in a nilpotent Lie group with a sub-Riemannian structure are obtained. All the results are new and have theoretical and practical significance. They can be applied in the study of concrete mathematical problems as well as in mathematical modeling of real processes. The results of the research are published in 15 scientific papers, in 1 theses, in 43 contributions for international mathematical conferences, 12 papers are prepared for publication. Product Description popup.authors Є. Петров І. Рижкова-Герасимова В. Гордевський В. Коробов Г. Скляр К. Несвіт М. Бебія М. Трощій Н. Кізілова О. Резуненко О. Щербина С. Ігнатович С. Жученко Т. Ревіна popup.nrat_date 2020-04-02 Close